Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
432 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#20263877 | C2 | semidirect |
| 3. #27163878 | C2 | semidirect |
| 4. #27163781 | C2 | semidirect |
| 5. C23×C8×C199 | C2 | semidirect |
| 9. #20263929 | C4 | semidirect |
| 46. C2×C8×C199 | D4 | semidirect |
| 82. C22×C199 | #102 | semidirect |
| 106. C199 | #1893 | semidirect |
| 108. C23×C8 | D199 | semidirect |
| 147. C2×C8 | C22⋊D199 | semidirect |
| 194. C22 | #20263877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263929 | 2 |
| C2×#20263877 | 2 |
| #27163878 | 2 |
| #27163781 | 2 |
| C23×C8×C199 | 2 |
| #1893 | 199 |